• Why is mathematics required in school?
From some skeptics:
• How much high school mathematics can all students be expected to learn?
• What's wrong with ability grouping and vocational tracking?
• Don't calculators do more harm than good?
• Aren't "open-ended" problems just an invitation to sloppy thinking?
From other skeptics:
• Doesn't "communication" belong in English class rather than in math class?
• Why waste time in math class on investigations and experiments?
• How can students be expected to "solve problems" before they have mastered basic skills?
• Doesn't every mathematics problem have a single correct answer?
From some friends:
• Why should students have to "construct" mathematics for themselves?
• Don't students deserve to be taught by teachers rather than by other students?
• What good is "thinking mathematically" if students can't calculate tips or solve equations?
• Is understanding a realistic (or even desirable) goal of school mathematics?
From other friends:
• Does mastery of skills lead to understanding?
• Does understanding lead to mastery of skills?
• Can mathematical reasoning be taught?
• How important are proofs for school mathematics?
• How important is it that problems be set in authentic contexts?
• How can students learn to recognize and use mathematics outside of mathematics class?
• How many mathematics are there?